On the numerical treatment and analysis of finite deformation ductile single crystal plasticity

This contribution is concerned with the numerical analysis and simulation of instability phenomena such as shearband localization in plastic flow processes within the framework of ductile single (fee) crystal viscoplasticity. To this end, a family of implicit constitutive algorithms and their implementation are considered in detail. Issues of accuracy and conservation of plastic incompressibility are examined. Moreover, the implementation within an overall Newton-Raphson finite element solution strategy relies an the correct evaluation of the algorithmic tangent moduli which result from linearizing the stress update integrator. Likewise, these algorithmic tangent moduli are employed within the numerical analysis of the spatial localization tenser. Examples demonstrating the performance of the proposed strategy at the local constitutive level as well as at the global structural level are given.